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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

The Anti-de Sitter proof of Thurston's earthquake theorem

Farid Diaf
  • Fonction : Auteur
Andrea Seppi
  • Fonction : Auteur

Résumé

Thurston's earthquake theorem asserts that every orientation-preserving homeomorphism of the circle admits an extension to the hyperbolic plane which is a (left or right) earthquake. The purpose of these notes is to provide a proof of Thurston's earthquake theorem, using the bi-invariant geometry of the Lie group PSL(2,R), which is also called Anti-de Sitter three-space. The involved techniques are elementary, and no background knowledge is assumed apart from some two-dimensional hyperbolic geometry.
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hal-04235471 , version 1 (11-10-2023)

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Farid Diaf, Andrea Seppi. The Anti-de Sitter proof of Thurston's earthquake theorem. 2023. ⟨hal-04235471⟩
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